Method of Moments parameter estimation. Consider a probability model characterizing the return on the market. The model corresponded to a version of the Poisson mixture of normals we have been studying. Denote the return in time period t as rt. The arrival of an extraordinary event or "disaster" is governed by a Poisson random variable, j = {0, 1, 2, 3, . . .}, with an intensity parameter . When j = 0 the disaster is avoided, and we interpret larger values of j as the arrival of disasters of increasing magnitude, i.e., j = 2 is a bigger disaster than j = 1. Assume that at each time period, rt follows a normal distribution with mean j, and variance 2 (i.e., the mean shifts with the value of j, but the variance stays the same), for constant parameters > 0, , and > 0. (a) What are the first four cumulants of rt as a function of the parameters > 0, , , and ? (b) We will now combine these theoretical values with the corresponding sample values you calculated in Questions 1(b) to calibrate or estimate the unknown parameters of the model